TSTP Solution File: SYO030^1 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO030^1 : TPTP v8.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 21 19:29:38 EDT 2022
% Result : Theorem 6.14s 6.33s
% Output : Proof 6.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 16
% Syntax : Number of formulae : 21 ( 10 unt; 1 typ; 2 def)
% Number of atoms : 38 ( 2 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 57 ( 20 ~; 8 |; 0 &; 15 @)
% ( 6 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 10 con; 0-2 aty)
% Number of variables : 13 ( 3 ^ 10 !; 0 ?; 13 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_eigen__3,type,
eigen__3: $o ).
thf(h0,assumption,
! [X1: $o > $o,X2: $o] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: $o] :
~ ~ ! [X2: $o > $o] :
( ( X2 @ ~ X1 )
=> ( X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(sP1,plain,
( sP1
<=> ( ~ eigen__3
=> eigen__3 ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: $o] :
~ ! [X2: $o > $o] :
( ( X2 @ ~ X1 )
=> ( X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> eigen__3 ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $o > $o] :
~ ! [X2: $o] :
~ ! [X3: $o > $o] :
( ( X3 @ ( X1 @ X2 ) )
=> ( X3 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( sP3
=> ~ sP3 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: $o > $o] :
( ( X1 @ ~ sP3 )
=> ( X1 @ sP3 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(def_leibeq,definition,
( leibeq
= ( ^ [X1: $o,X2: $o] :
! [X3: $o > $o] :
( ( X3 @ X1 )
=> ( X3 @ X2 ) ) ) ) ).
thf(conj,conjecture,
~ sP4 ).
thf(h1,negated_conjecture,
sP4,
inference(assume_negation,[status(cth)],[conj]) ).
thf(1,plain,
( ~ sP1
| sP3
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP5
| ~ sP3
| ~ sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP6
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP6
| sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( sP2
| sP6 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(6,plain,
( ~ sP4
| ~ sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,h1]) ).
thf(8,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[7,h0]) ).
thf(0,theorem,
~ sP4,
inference(contra,[status(thm),contra(discharge,[h1])],[7,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO030^1 : TPTP v8.1.0. Released v3.7.0.
% 0.12/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jul 9 15:54:22 EDT 2022
% 0.12/0.33 % CPUTime :
% 6.14/6.33 % SZS status Theorem
% 6.14/6.33 % Mode: mode506
% 6.14/6.33 % Inferences: 681275
% 6.14/6.33 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------